Length Definition and 1000 Threads

Homework Statement A Koenig eyepiece with a focal length of 100mm is constructed in the following way: The first lens is made of 755276 glass which is 10 mm thick on axis. The radius of curvature of its left hand surface is -225mm, the radius of curvature of it right hand surface is 83.6...

is it logical to ask this question in Spherical coordinates: Using the differential length dl , find the length where r=1 0<Θ<∏/4 ∏/2< θ <∏/4 where Θ is the azimuthal angle. What I mean by ∏/2< θ <∏/4 is that the line is a "diagonal" line which has an ascention of ∏/4 from the xy...

This may seem like a dumb question, but is finding the "arc length" of a curve and finding the "length" of a curve the same thing? Just worded differently?

The three main effects of SR occur in inertial frames and change the description of space-time relative to a particular observer. My question here is how do these effects occur on Earth, since we know that motion on Earth is non-inertial. I know that we travel at small speeds and that we can't...

Hello, I would like to know how to calculate how long the phase transition when cooling lasts. So basically how long the latent transition lasts. I really don't have any ideas how this could be calculated, although I would assume it is function of the mass. Any help is much appreciated.

Hello, I solved the arc length for a particular problem. However, what is the unit of arc length if the units of the velocity vs time graph are m/s vs s? I am really confused.

Hi all. This is my first time posting so forgive me If I am doing something wrong. I am a year 7 student interested in all types of physics and my question is, if nothing can be smaller than Planck length then wouldn't past a certain point the digits of pi become obsolete? Simply because the...

Homework Statement Two converging lenses of the same focal length f are separated by distance 2f. The axis of the second lens is inclined at angle θ = 60º with respect to the axis of the first lens. A parallel paraxial beam of light is incident from left side of the lens. Then: (A)...

I see on StackOverflow people doing stuff like [FONT="Courier New"] for (int k = 0; k < something.length(); k++) where the body of the for loop never has any chance of modify something's length. I thought that was considered bad coding practice. The implementation of something's class might...

Here is the question: I have posted a link there to this thread so the OP can view my work.

1. The problem statement, all variables and given/known If C is a smooth curve given by r(s)= x(s)i + y(s)j + z(s)k Where s is the arc length parameter. Then ||r'(s)|| = 1. My professor has stated that this is true for all cases the magnitude of r'(s) will always equal 1. But he wants me...

Most of us are familiar with the fact that in Loop gravity the area and volume observables have discrete spectrum. The discrete spectrum of the area operator, leading to a smallest positive measurable area, has lots of mathematical consequences that have been derived in the theory. It helps...

Homework Statement Hi everyone, the problem I'm stuck on reads: " Imagine a solenoid 3m in diameter, 5m long having 1164 turns of super conducting cable. What length of super conducting cable is used to wind this solenoid?"Homework Equations Circumference = 2pi*radiusThe Attempt at a Solution...

What should it be, {sin(ωt-\frac{k}{n}x)} or {sin(ωt-nkx)}? I am contemplating this with respect to the proper waveform in a medium, following specific rules, particularly when it comes to the dispersion relation and ultimately what this would mean in the context of the Lorentz transformations...

Find the exact length of the curve $0 \le x \le 1$ $$y = 1 + 6x^{\frac{3}{2}}$$ <-- If you can't read this, the exponent is $$\frac{3}{2}$$ $$ \therefore y' = 9\sqrt{x}$$ $$\int ^1_0 \sqrt{1 + (9\sqrt{x})^2} \, dx$$ $$= \int ^1_0 \sqrt{1 + 81x} \, dx$$ $$ = \int^1_0 1 + 9\sqrt{x} \...

A little bit confused. Find the exact length of the curve $$y = \frac{1}{4}x^2 - \frac{1}{2}\ln x$$ $$1 \le x \le 2$$ Using the formula: $$y = \sqrt{1 + (\frac{dy}{dx})^2} \, dx$$ I obtained this: $$\int ^2_1 \sqrt{ \frac{1}{2} + \frac{x^2}{4} + \frac{1}{4x^2}}$$ Now my problem is...

Consider an oblique circular cone of altitude h, base radius R, with apex directly above a point on the base circumference. What is the mean length (& variance) for the set of all rays from the apex to points on or within the base circumference?

Hello, question about the energy of a variable length pendulum. Suppose you have a pendulum in the standard sense where θ is the angle, and we let the length r be a function of time r = r(t). What is the energy of the pendulum? So far, I have determined that kinetic energy is =...

[FONT=Helvetica Neue]A closed organ pipe has a length of 2.40 m. [FONT=Helvetica Neue]a.) What is the frequency of the note played by the pipe? Use [FONT=Helvetica Neue]343 m/s as the speed of sound. [FONT=Helvetica Neue]b.) When a second pipe is played at the same time, a 1.40 Hz beat note...

Hi all, I tried searching for this but failed to find an answer to my question. I am having an issue with properly interpreting the equations for time dilation and length contraction. Let's assume that I am standing still and a train is passing by next to me (moving with uniform velocity). Let...

Homework Statement What is the tension of the string? Mass of piano string- 3.5g Lenght of piano string- 75cm Fundamental frecuency- 469Hz Homework Equations λ=2L/n ? Dont know where to start.

Homework Statement I have a lot of information about 2 different superconductor materials; indium and lead. The indium is pretty much 100% indium with no impurities, and the lead is unknown purity. I have the temperatures and magnetic fields at which they are superconducting and the...

I'm interested in modeling a system where the material varies along its length, thus the conductivity coefficient would be a function of both T, and x. k(T,x). For starters, if I assume negligible change w.r.t T, then he heat diffusion equation would be d/dt(k(x)dT/dx)=0. Correct? What if k just...

Find the length of the positive arc of the curve y=cosh^{-1}(x) (for which y≥0) between x=1 and x=\sqrt{5}. My attempt: x=cosh(y) → \frac{dx}{dy} = sinh(y) → (\frac{dx}{dy})^{2}=sinh^{2}(y), so ds=dy\sqrt{1+sinh^{2}(y)}, therefore the arc length is S=\int_{y=0}^{y=cosh^{-1}(\sqrt{5})} cosh(y)...

Homework Statement Show that the experiment depicted in Figure 2.11 and discussed in the text leads directly to the derivation of length contraction. Figure 2.11: Homework Equations d=v*t Requested result: L=L0\sqrt{1-\frac{v^2}{c^2}} The Attempt at a Solution In K the...

http://chestofbooks.com/home-improvement/woodworking/Handicraft-For-Boys/images/Making-the-Model-Engine-292.png I want to know how you would determine how long the rocker arm in this picture is...

Homework Statement Light from infinity strikes a diffracting grating normally with 600 lines per mm. The emitted light then passes through a lens to project visible light (400-800 nm) spectrum onto a screen that is 50mm, just enough to cover it. Find the focal length of the lens. Homework...

The solution to this question (whose answer is pi) is eluding me: The radius of a circle is 3 feet. Find the approximate length of an arc of this circle, if the length of the chord of the arc is 3 feet also.

Homework Statement We calculated times of the periods of varying pendulum lengths. (20cm, 40cm, 60cm, 80cm). Then the frequency was calculated for each length and then a frequency-length graph was made. Since the graph is an exponential relationship we graphed our values on a log-log chart...

I had a quick question about Time Dilation and Length Contraction. Are the two just different ways of measuring/describing the same effect? Or rather they both follow as a consequence from one another? i.e. I can find how much a length is contracted by finding the dilated time interval and...

how do i integrate the function sqrt(1 + 1/2(y^1/2 - y^(-1/2))^2) from 0 to 1??

Homework Statement A long string with a mass/length of 500g/m is placed under a tension of 400N. The string is then vibrated up and down with a period of .425sec. What is the wave speed? What is the wavelength of the resulting wave? I have no idea where to beginI would really...

Homework Statement Homework Equations The Attempt at a Solution I tried with the conservation laws. Angular momentum conservation won't work. To use energy conservation, I need the force pulling up the string but I don't have it. The force in the given case is tension but the tension...

Homework Statement We measured the time between a signal source, and it's reflection coming back through our probe after going through an open-ended coaxial cable. My teacher told us this: the cable has a polyethylene insulator between central wire and the grounding web, which has a...

Homework Statement So I am not sure how to multiply these two (A*R^2) together. Homework Equations A=( x^2 + y^2 + z^2 ) (xe + y e + z e ) Where x represents the three vector compones I also have R^2=x^2+y^2+z^2 The Attempt at a Solution Is the product of A (x^3e + y^3 e + z^3...

Hi, Suppose we're looking at a random sequence of digits from 0 to 9. We start off reading the digits until every digit from 0 to 9 has been seen at least once and we mark the count of digits read up to that point (run length). We then reset the run length and continue until the whole random...

I found a funny video on youtube, but I am not totally convinced by the argument. It says that a pure magnetic field caused by a current in a wire can lead to a combined electric + magnetic field in a moving frame. It explains more or less convincingly that this can be understood as a...

Imagine two asteroids which are separed by 1Ly distance. They are in uniform velocity (.9c) with respect to an observe in space. So from the observers point of view (rest frame), does the distance between the asteroids (ie. 1Ly) appear contracted?

https://dl.dropboxusercontent.com/u/260388836/index.html Let arrow height be 1cm. focal length:1cm So if I move the arrow to the focal point,image is not formed.(i.e formed at infinity) But, Lets move it to say 0.999 Now the image is virtual and is magnified to about 1000X If I make it...

Homework Statement Attached Homework Equations The Attempt at a Solution I am to provide a solution without using any trigonometry or calculus, but I can't find a way. To clarify, I must find d(x). Involving trig, the problem is trivial, as the angle "A" is equal to...

What is "Correlation length"? Hi everyone, I want to know meaning of "correlation length". Correlation function is usually used in statistics, so I think correlation length also similar meaning. But some paper used correlation length to explain roughness factor. Plz, anyone reply...

Homework Statement The length L or the curve given by \frac{3y^{4}}{2}+\frac{1}{48y^{2}}-5 from y=1 to y=2 Homework Equations The Attempt at a Solution Setting up the formula is easy. First I found the derivative of f(y) which is: f'(y)=6y^{3}-\frac{1}{24y^{3}} Then I plugged...

I am currently designing a convergent nozzle for use in experiments and wanted to check something: Will the pressure and density of the flow always expand to ambient (following the isentropic relations) when it reaches the nozzle exit regardless of nozzle contraction ratio and length? Any...

I have just started studying Special Relativity in class and the concepts of Proper Length and Proper Time are giving me some issues. I understand the basics of length contraction and time dilation, but the idea of this "proper" time and length is giving me problems. One example in particular...

I would appreciate views on the following understanding of length and distance in SR, restricted here to inertial movement. This is the beginning of a follow up to the thread: https://www.physicsforums.com/showthread.php?t=724025 1. The spatial length of an object is the spatial separation...

Homework Statement find the length of a circular helix expressed in parametric form x= cos(t), y=sin(t) and z = t from t = 0 to t =2pi Homework Equations L = integrate ds (ds)^2 = (dx)^2+(dy)^2+(dz)^2 The Attempt at a Solution I got to ds = (1 + (dt)^2)^0.5 but I can't...

Homework Statement Find the length of the curve y = x^3/a^2 + a^2/12x between a and a/2 Homework Equations Length L = integrate (1+ dy/dx)^2)^0.5 The Attempt at a Solution I got to integrate (9x^4/a^2 + 1/2 + a^4/144x^4)^0.5 but I can't simplify it

I will be graduating with an engineering degree (mechanical) in May of 2014. The city that I currently live in is not where I want to stay after I graduate; however, my wife is well established in her career and it makes sense for us to stay here for a year or so in order to save up money etc...

If an object is going at near C(light velocity) and undergoes length contraction. Does the mass fluctuate?I apologize if it is an obvious question but I'm a little rusty on my physics.

The problem is to a.) solve for the slope m of the hypotenuse of the right triangle indicated by the shaded area, and b.) solve for the length of the hypotenuse, if possible. I made a mistake in transcribing the problem onto paper, the line of course extends indefinitely but the shaded area and...